Electrostatics – JEE Mains Physics
1. Electric Charges
- Electric charges are conserved, meaning the total charge in an isolated system remains constant.
- Coulomb’s Law describes the force between two point charges as:
F = k * (q₁ * q₂) / r²
where q₁ and q₂ are the charges, r is the distance between them, and k is Coulomb's constant. - The superposition principle states that the net force on a charge due to multiple other charges is the vector sum of the forces from each individual charge.
2. Electric Field
- The electric field (E) due to a point charge is given by:
E = k * q / r²
where q is the charge and r is the distance from the charge. - Electric field lines represent the direction of the electric field and indicate how positive test charges would move in the field.
- An electric dipole consists of two equal and opposite charges separated by a distance, and the field due to a dipole can be calculated based on its moment.
3. Torque on a Dipole in a Uniform Electric Field
- A dipole experiences a torque in a uniform electric field, which tends to align the dipole with the field.
- The torque (τ) on a dipole is given by:
τ = pE sin(θ)
where p is the dipole moment, E is the electric field, and θ is the angle between p and E.
4. Electric Flux and Gauss's Law
- Electric flux (Φ) is the product of the electric field and the area through which the field lines pass:
Φ = E * A * cos(θ)
where E is the electric field, A is the area, and θ is the angle between the field and the normal to the surface. - Gauss’s law relates the electric flux through a closed surface to the charge enclosed by the surface:
∮ E · dA = (Q_enclosed / ε₀)
where ε₀ is the permittivity of free space.
5. Applications of Gauss's Law
- Gauss's law can be used to find the electric field due to infinitely long uniformly charged straight wires, uniformly charged infinite plane sheets, and uniformly charged thin spherical shells.
6. Electric Potential
- The electric potential (V) due to a point charge is given by:
V = k * q / r
where q is the charge and r is the distance from the charge. - The potential difference between two points is the work done in moving a charge between those points.
7. Equipotential Surfaces
- Equipotential surfaces are surfaces where the electric potential is constant. No work is done when a charge moves along an equipotential surface.
8. Electric Potential Energy
- The electric potential energy of a system of two point charges is given by:
U = k * (q₁ * q₂) / r
where q₁ and q₂ are the charges, and r is the distance between them. - The potential energy of an electric dipole in an electric field is given by:
U = -pE cos(θ)
where p is the dipole moment, E is the electric field, and θ is the angle between p and E.
9. Conductors and Insulators
- Conductors are materials that allow the free flow of electric charge (e.g., metals), while insulators prevent the flow of charge (e.g., rubber, wood).
10. Dielectrics and Electric Polarization
- Dielectrics are insulating materials that, when placed in an electric field, become polarized and reduce the effective field inside the material.
11. Capacitors and Capacitance
- A capacitor is a device used to store electric charge. The capacitance (C) of a capacitor is defined as:
C = Q / V
where Q is the charge stored and V is the potential difference across the plates.
12. Combination of Capacitors
- Capacitors can be combined in series or parallel:
- Series combination: 1 / C_total = 1 / C₁ + 1 / C₂ + ...
- Parallel combination: C_total = C₁ + C₂ + ...
13. Capacitance of a Parallel Plate Capacitor
- The capacitance of a parallel plate capacitor with a dielectric medium between the plates is given by:
C = (ε₀ * A) / d
where A is the area of the plates, d is the distance between them, and ε₀ is the permittivity of free space.
14. Energy Stored in a Capacitor
- The energy (U) stored in a capacitor is given by:
U = (1/2) * C * V²
where C is the capacitance and V is the potential difference across the capacitor.